The 20-year-old has had to content himself with a place on the Basel bench of late; he has not started any of the club's last four matches.
He has taken the opportunity to impress from the bench, however, by scoring a vital equaliser in the Champions League against Barcelona and striking twice after being introduced five days later against Vaduz.
The Swiss international, who was a prominent performer during a lax showing from the hosts at Euro 2008, has reportedly caught the eye of a number of European clubs, with Hoofenheim also registering interest.
The player himself favours a move to Germany and is eyeing a transfer to the BayArena with Leverkusen.
He told Kicker: "It is absolutely normal to want to move abroad at some time and I see the best chances for me personally and for my game in Leverkusen."
The Werkself have been eager to snare the forward since the summer, but have as yet failed to agree a fee with Basel. It is believed that a bid of €8 million would force the hand of Christian Gross' side.
Leverkusen's general manager Michael Reschke is optimistic of tying up the loose ends of a deal in the near future.
He told the press: "It is a matter for negotiations.
"We would like to sign Eren on 1st January, but if this isn't possible then we can wait until the summer. We want to reach an agreement with FC Basel soon."